Skip to main content
SpringerLink
Log in

Tightly Secure Hierarchical Identity-Based Encryption

  • Conference paper
  • First Online:
Public-Key Cryptography – PKC 2019 (PKC 2019)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 11442))

Included in the following conference series:

Abstract

We construct the first tightly secure hierarchical identity-based encryption (HIBE) scheme based on standard assumptions, which solves an open problem from Blazy, Kiltz, and Pan (CRYPTO 2014). At the core of our constructions is a novel randomization technique that enables us to randomize user secret keys for identities with flexible length.

The security reductions of previous HIBEs lose at least a factor of \( Q \), which is the number of user secret key queries. Different to that, the security loss of our schemes is only dependent on the security parameter. Our schemes are adaptively secure based on the Matrix Diffie-Hellman assumption, which is a generalization of standard Diffie-Hellman assumptions such as \(k\)-Linear. We have two tightly secure constructions, one with constant ciphertext size, and the other with tighter security at the cost of linear ciphertext size. Among other things, our schemes imply the first tightly secure identity-based signature scheme by a variant of the Naor transformation.

J. Pan—Supported by DFG grant HO 4534/4-1.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 69.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 89.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    Here we ignore the additive negligible terms for simplicity.

  2. 2.

    In this paper, we do not distinguish almost tight security from tight security, but we will detail the security loss in the security proof and comparison of our schemes.

  3. 3.

    A different bitlength on each level is possible as well, but we assume it is \(\alpha \) on each level to ease notation.

  4. 4.

    The same technique can be used to prove the IBE of [3] secure with duplicated \(\textsc {Ext}\)-queries. Thus they work without a pseudorandom function.

References

  1. Abe, M., Hofheinz, D., Nishimaki, R., Ohkubo, M., Pan, J.: Compact structure-preserving signatures with almost tight security. In: Katz, J., Shacham, H. (eds.) CRYPTO 2017. LNCS, vol. 10402, pp. 548–580. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-63715-0_19

    Chapter  Google Scholar 

  2. Bader, C., Hofheinz, D., Jager, T., Kiltz, E., Li, Y.: Tightly-secure authenticated key exchange. In: Dodis, Y., Nielsen, J.B. (eds.) TCC 2015. LNCS, vol. 9014, pp. 629–658. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-46494-6_26

    Chapter  Google Scholar 

  3. Blazy, O., Kiltz, E., Pan, J.: (Hierarchical) identity-based encryption from affine message authentication. In: Garay, J.A., Gennaro, R. (eds.) CRYPTO 2014. LNCS, vol. 8616, pp. 408–425. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-662-44371-2_23

    Chapter  Google Scholar 

  4. Boneh, D., Franklin, M.: Identity-based encryption from the weil pairing. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 213–229. Springer, Heidelberg (2001). https://doi.org/10.1007/3-540-44647-8_13

    Chapter  Google Scholar 

  5. Canetti, R., Halevi, S., Katz, J.: Chosen-ciphertext security from identity-based encryption. In: Cachin, C., Camenisch, J.L. (eds.) EUROCRYPT 2004. LNCS, vol. 3027, pp. 207–222. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-24676-3_13

    Chapter  Google Scholar 

  6. Chen, J., Gay, R., Wee, H.: Improved dual system ABE in prime-order groups via predicate encodings. In: Oswald, E., Fischlin, M. (eds.) EUROCRYPT 2015. LNCS, vol. 9057, pp. 595–624. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-46803-6_20

    Chapter  Google Scholar 

  7. Chen, J., Lim, H.W., Ling, S., Wang, H., Wee, H.: Shorter IBE and signatures via asymmetric pairings. In: Abdalla, M., Lange, T. (eds.) Pairing 2012. LNCS, vol. 7708, pp. 122–140. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-36334-4_8

    Chapter  Google Scholar 

  8. Chen, J., Wee, H.: Fully, (Almost) tightly secure IBE and dual system groups. In: Canetti, R., Garay, J.A. (eds.) CRYPTO 2013. LNCS, vol. 8043, pp. 435–460. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-40084-1_25

    Chapter  Google Scholar 

  9. Cocks, C.: An identity based encryption scheme based on quadratic residues. In: Honary, B. (ed.) Cryptography and Coding 2001. LNCS, vol. 2260, pp. 360–363. Springer, Heidelberg (2001). https://doi.org/10.1007/3-540-45325-3_32

    Chapter  Google Scholar 

  10. Escala, A., Herold, G., Kiltz, E., Ràfols, C., Villar, J.: An algebraic framework for Diffie-Hellman assumptions. In: Canetti, R., Garay, J.A. (eds.) CRYPTO 2013. LNCS, vol. 8043, pp. 129–147. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-40084-1_8

    Chapter  Google Scholar 

  11. Gay, R., Hofheinz, D., Kiltz, E., Wee, H.: Tightly CCA-secure encryption without pairings. In: Fischlin, M., Coron, J.-S. (eds.) EUROCRYPT 2016. LNCS, vol. 9665, pp. 1–27. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-49890-3_1

    Chapter  Google Scholar 

  12. Gay, R., Hofheinz, D., Kohl, L., Pan, J.: More efficient (almost) tightly secure structure-preserving signatures. In: Nielsen, J.B., Rijmen, V. (eds.) EUROCRYPT 2018. LNCS, vol. 10821, pp. 230–258. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-78375-8_8

    Chapter  Google Scholar 

  13. Gentry, C.: Practical identity-based encryption without random oracles. In: Vaudenay, S. (ed.) EUROCRYPT 2006. LNCS, vol. 4004, pp. 445–464. Springer, Heidelberg (2006). https://doi.org/10.1007/11761679_27

    Chapter  Google Scholar 

  14. Gentry, C., Silverberg, A.: Hierarchical ID-based cryptography. In: Zheng, Y. (ed.) ASIACRYPT 2002. LNCS, vol. 2501, pp. 548–566. Springer, Heidelberg (2002). https://doi.org/10.1007/3-540-36178-2_34

    Chapter  Google Scholar 

  15. Gong, J., Cao, Z., Tang, S., Chen, J.: Extended dual system group and shorter unbounded hierarchical identity based encryption. Des. Codes Crypt. 80(3), 525–559 (2016). https://doi.org/10.1007/s10623-015-0117-z

    Article  MathSciNet  MATH  Google Scholar 

  16. Gong, J., Dong, X., Chen, J., Cao, Z.: Efficient IBE with tight reduction to standard assumption in the multi-challenge setting. In: Cheon, J.H., Takagi, T. (eds.) ASIACRYPT 2016. LNCS, vol. 10032, pp. 624–654. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-53890-6_21

    Chapter  Google Scholar 

  17. Hesse, J., Hofheinz, D., Kohl, L.: On tightly secure non-interactive key exchange. In: Shacham, H., Boldyreva, A. (eds.) CRYPTO 2018, Part II. LNCS, vol. 10992, pp. 65–94. Springer, Heidelberg (Aug (2018)

    Google Scholar 

  18. Hofheinz, D., Jager, T.: Tightly secure signatures and public-key encryption. In: Safavi-Naini, R., Canetti, R. (eds.) CRYPTO 2012. LNCS, vol. 7417, pp. 590–607. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-32009-5_35

    Chapter  Google Scholar 

  19. Hofheinz, D., Jia, D., Pan, J.: Identity-based encryption tightly secure under chosen-ciphertext attacks. In: Peyrin, T., Galbraith, S. (eds.) ASIACRYPT 2018. LNCS, vol. 11273, pp. 190–220. Springer, Cham (2018). https://doi.org/10.1007/978-3-030-03329-3_7

    Chapter  Google Scholar 

  20. Hofheinz, D., Kiltz, E.: Secure hybrid encryption from weakened key encapsulation. In: Menezes, A. (ed.) CRYPTO 2007. LNCS, vol. 4622, pp. 553–571. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-74143-5_31

    Chapter  Google Scholar 

  21. Hofheinz, D., Koch, J., Striecks, C.: Identity-based encryption with (almost) tight security in the multi-instance, multi-ciphertext setting. In: Katz, J. (ed.) PKC 2015. LNCS, vol. 9020, pp. 799–822. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-46447-2_36

    Chapter  Google Scholar 

  22. Horwitz, J., Lynn, B.: Toward hierarchical identity-based encryption. In: Knudsen, L.R. (ed.) EUROCRYPT 2002. LNCS, vol. 2332, pp. 466–481. Springer, Heidelberg (2002). https://doi.org/10.1007/3-540-46035-7_31

    Chapter  Google Scholar 

  23. Jutla, C.S., Roy, A.: Shorter quasi-adaptive NIZK proofs for linear subspaces. In: Sako, K., Sarkar, P. (eds.) ASIACRYPT 2013. LNCS, vol. 8269, pp. 1–20. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-42033-7_1

    Chapter  Google Scholar 

  24. Kiltz, E., Neven, G.: Identity-based signatures. In: Joye, M., Neven, G. (eds.) Identity-Based Cryptography. IOS Press, Amsterdam (2009)

    MATH  Google Scholar 

  25. Kiltz, E., Pan, J., Wee, H.: Structure-preserving signatures from standard assumptions, revisited. In: Gennaro, R., Robshaw, M. (eds.) CRYPTO 2015. LNCS, vol. 9216, pp. 275–295. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-48000-7_14

    Chapter  Google Scholar 

  26. Kiltz, E., Wee, H.: Quasi-adaptive NIZK for linear subspaces revisited. In: Oswald, E., Fischlin, M. (eds.) EUROCRYPT 2015. LNCS, vol. 9057, pp. 101–128. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-46803-6_4

    Chapter  Google Scholar 

  27. Lewko, A.: Tools for simulating features of composite order bilinear groups in the prime order setting. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT 2012. LNCS, vol. 7237, pp. 318–335. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-29011-4_20

    Chapter  MATH  Google Scholar 

  28. Lewko, A., Waters, B.: Why proving HIBE systems secure is difficult. In: Nguyen, P.Q., Oswald, E. (eds.) EUROCRYPT 2014. LNCS, vol. 8441, pp. 58–76. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-642-55220-5_4

    Chapter  Google Scholar 

  29. Naor, M., Reingold, O.: On the construction of pseudo-random permutations: Luby-Rackoff revisited (extended abstract). In: 29th ACM STOC, pp. 189–199. ACM Press, May 1997

    Google Scholar 

  30. Sakai, R., Ohgishi, K., Kasahara, M.: Cryptosystems based on pairing. In: SCIS 2000, Okinawa, Japan, January 2000

    Google Scholar 

  31. Shamir, A.: Identity-based cryptosystems and signature schemes. In: Blakley, G.R., Chaum, D. (eds.) CRYPTO 1984. LNCS, vol. 196, pp. 47–53. Springer, Heidelberg (1985). https://doi.org/10.1007/3-540-39568-7_5

    Chapter  Google Scholar 

  32. Waters, B.: Dual system encryption: realizing fully secure IBE and HIBE under simple assumptions. In: Halevi, S. (ed.) CRYPTO 2009. LNCS, vol. 5677, pp. 619–636. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-03356-8_36

    Chapter  Google Scholar 

  33. Waters, B.: Efficient identity-based encryption without random oracles. In: Cramer, R. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 114–127. Springer, Heidelberg (2005). https://doi.org/10.1007/11426639_7

    Chapter  Google Scholar 

  34. Wee, H.: Dual system encryption via predicate encodings. In: Lindell, Y. (ed.) TCC 2014. LNCS, vol. 8349, pp. 616–637. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-642-54242-8_26

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Karlsruhe Institute of Technology, Karlsruhe, Germany

    Roman Langrehr & Jiaxin Pan

Authors
  1. Roman Langrehr
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jiaxin Pan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Roman Langrehr .

Editor information

Editors and Affiliations

  1. SKLOIS, Institute of Information Engineering, Chinese Academy of Sciences, Beijing, China

    Dongdai Lin

  2. Security Research Laboratories, NEC Corporation, Kawasaki, Japan

    Kazue Sako

Rights and permissions

Reprints and permissions

Copyright information

© 2019 International Association for Cryptologic Research

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Langrehr, R., Pan, J. (2019). Tightly Secure Hierarchical Identity-Based Encryption. In: Lin, D., Sako, K. (eds) Public-Key Cryptography – PKC 2019. PKC 2019. Lecture Notes in Computer Science(), vol 11442. Springer, Cham. https://doi.org/10.1007/978-3-030-17253-4_15

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-17253-4_15

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-17252-7

  • Online ISBN: 978-3-030-17253-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Societies and partnerships

Search

Navigation